Limit $F$-signature functions of two-variable binomial hypersurfaces

Abstract

The $F$-signature is a fundamental numerical invariant of singularities in positive characteristic. Its positivity detects strong $F$-regularity, an important class of singularities related to KLT singularities in characteristic zero. In this paper, we compute the limiting $F$-signature function of binomial and other related hypersurfaces in two variables as the characteristic $p\to \infty$. In particular, we show it is a piecewise polynomial function, and relate it to the normalized volume.

Added discussions connecting to Han's thesis (including Remark 5.5) + minor improvements. 29 pages, 3 figures

References in corpus (9)

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